Electroencephalography (EEG) is among the most widely diffused, inexpensive, and adopted neuroimaging techniques. Nonetheless, EEG requires measurements against a reference site(s), which is typically chosen by the experimenter, and specific pre-processing steps precede analyses. It is therefore valuable to obtain quantities that are minimally affected by reference and pre-processing choices. Here, we show that the topological structure of embedding spaces, constructed either from multi-channel EEG timeseries or from their temporal structure, are subject-specific and robust to re-referencing and pre-processing pipelines. By contrast, the shape of correlation spaces, that is, discrete spaces where each point represents an electrode and the distance between them that is in turn related to the correlation between the respective timeseries, was neither significantly subject-specific nor robust to changes of reference. Our results suggest that the shape of spaces describing the observed configurations of EEG signals holds information about the individual specificity of the underlying individual's brain dynamics, and that temporal correlations constrain to a large degree the set of possible dynamics. In turn, these encode the differences between subjects' space of resting state EEG signals. Finally, our results and proposed methodology provide tools to explore the individual topographical landscapes and how they are explored dynamically. We propose therefore to augment conventional topographic analyses with an additional-topological-level of analysis, and to consider them jointly. More generally, these results provide a roadmap for the incorporation of topological analyses within EEG pipelines.

Cognitive Computational Neuroscience Group Institute for Computer Science University of Bern Bern Switzerland

Department of Complex Systems Institute for Computer Science Czech Academy of Science Prague Czechia

Department of Hearing and Speech Sciences Vanderbilt University Nashville TN USA

Department of Ophthalmology Fondation Asile des aveugles and University of Lausanne Lausanne Switzerland

EEG CHUV UNIL Section CIBM Center for Biomedical Imaging Lausanne Switzerland

ISI Foundation Turin Italy

ISI Global Science Foundation New York NY USA

Laboratory for Investigative Neurophysiology Department of Radiology Lausanne University Hospital and University of Lausanne Lausanne Switzerland

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